01 - Melt butter in a large pot over medium heat. Add onion, celery, and carrots. Sauté for 4-5 minutes until softened and fragrant.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to burn.
03 - Sprinkle flour into the pot and cook for 2 minutes, stirring constantly to form a smooth roux and eliminate raw flour taste.
04 - Gradually whisk in chicken broth, ensuring no lumps form. Bring mixture to a gentle simmer while whisking continuously.
05 - Add cooked chicken, thyme, salt, and pepper. Simmer for 15 minutes until vegetables are completely tender and flavors meld.
06 - Reduce heat to low. Stir in whole milk and heavy cream. Heat gently for 5 minutes, ensuring soup does not reach boiling point to prevent curdling.
07 - Add fresh parsley and adjust seasoning to taste. Serve hot in bowls, garnished with additional fresh parsley sprigs.